A275485 Number of integer lattice points from an n X n square in R^2 centered at the origin that are closer (measured using the Euclidean metric) to the origin than to any of the four sides of the square.

1, 1, 1, 1, 9, 9, 9, 9, 21, 25, 25, 25, 37, 45, 49, 49, 69, 69, 77, 81, 101, 109, 117, 117, 141, 149, 157, 165, 189, 197, 205, 213, 241, 261, 269, 269, 305, 321, 333, 341, 377, 385, 401, 413, 449, 465, 481, 489, 529, 545

Offset

1,5

Comments

There is a formula, but no closed form, for computing the entries of the sequence.

References

N. R. Baeth, L. Luther and R. McKee, Variations on a Putnam Problem, preprint, 2016.

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = (2*floor(n*(sqrt(2)-1)/2)+1)^2+4*Sum_{i=ceiling(-n*(sqrt(2)-1)/2)..floor(n*(sqrt(2)-1)/2)} ceiling(n/4-i^2/n)-1-floor(n*(sqrt(2)-1)/2).

Maple

A275485:=n->(2*floor(n*(sqrt(2)-1)/2)+1)^2+4*add(ceil(n/4-i^2/n)-1-floor(n*(sqrt(2)-1)/2), i=ceil(-n*(sqrt(2)-1)/2)..floor(n*(sqrt(2)-1)/2)): seq(A275485(n), n=1..100); # Wesley Ivan Hurt, Sep 27 2016

Prog

(PARI) a(n)=(2*floor(n*(sqrt(2)-1)/2)+1)^2+4*sum(i=ceil(-n*(sqrt(2)-1)/2), floor(n*(sqrt(2)-1)/2), ceil(n/4-i^2/n)-1-floor(n*(sqrt(2)-1)/2)); \\ Joerg Arndt, Sep 27 2016

Crossrefs

Cf. A000328.

Sequence in context: A068395 A245429 A242893 * A346263 A344337 A293832

Adjacent sequences: A275482 A275483 A275484 * A275486 A275487 A275488

Keyword

nonn

Author

Nicholas Baeth, Sep 26 2016

Status

approved